Question: Rewrite as a simplified fraction. ${1.7\overline{5} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 175.5555...\\ 10x &= 17.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 158}$ ${x = \dfrac{158}{90}} $ ${x = \dfrac{79}{45}} \text{or} {1 \dfrac{34}{45}}$